Thomassé, Stéphan Indivisibility and alpha-morphisms. (English) Zbl 0871.05055 Eur. J. Comb. 18, No. 4, 445-454 (1997). A relation \(R\) is \(p\)-divisible if for any partition of its basis into \(p+1\) subsets, \(R\) is embedded into the union of \(p\) subsets. This paper proves a generalization of an earlier result of M. Pouzet: any countable \(p\)-divisible relation embeds two copies of itself intersecting in at most \(p-1\) elements. The main tool of the proof is the notion of \(\alpha\)-morphism introduced in the theory of Ehrenfeucht-Fraïssé games. Reviewer: P.L.Erdös (Budapest) Cited in 1 Document MSC: 05D05 Extremal set theory 03E05 Other combinatorial set theory Keywords:divisibility of a relation; Rado’s graph; \(\Delta\)-system; Ehrenfeucht-Fraïssé games; \(\alpha\)-morphism PDFBibTeX XMLCite \textit{S. Thomassé}, Eur. J. Comb. 18, No. 4, 445--454 (1997; Zbl 0871.05055) Full Text: DOI Link